Finite Group Databasebeta

← C3×#10594760 #13174357

Subgroups — C3×#10594760 #13174357

Order 1728.

1230 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64319C211yesmaximal, characteristic
2C3×D32×Q8C211yesmaximal, characteristic, complemented
3C3×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#918C212yesmaximal, complemented
5C3×#63946C212yesmaximal, complemented
6C3×#63944C211yesmaximal, characteristic, complemented
7C3×#63943C212yesmaximal, complemented
8C3×#63940C211yesmaximal, characteristic, complemented
9C3×#63800C212yesmaximal, complemented
10C3×#63796C211yesmaximal, characteristic, complemented
11C3×#63791C211yesmaximal, characteristic, complemented
12C3×D3×#137—32nomaximal
13#10594760C311yesmaximal, characteristic, direct product factor
14C3×Q8×C3⋊D3C2211yescharacteristic
15C3×Q8×C3⋊D3C2211yescharacteristic
16C32×#239C2212yes—
17C32×D3×Q8C2212yescomplemented
18C3×#3802—21no—
19C3×#3802C2211yescharacteristic
20C3×C4×D32—21no—
21C3×C4×D32—21no—
22C3×C4×D32C2211yescharacteristic
23C3×#3797—21no—
24C3×#3797C2211yescharacteristic
25C3×#3795—22no—
26C3×#3795C2212yes—
27C3×D3×Dic6—22no—
28C3×D3×Dic6C2212yescomplemented
29C33×Q16C2211yescharacteristic, complemented
30C3×#3756C2211yescharacteristic, complemented
31C3×#3756C2211yescharacteristic, complemented
32C3×#3746C2211yescharacteristic, complemented
33C3×C8×C3⋊D3C2211yescharacteristic
34C32×#216C2212yescomplemented
35C32×#215C2212yescomplemented
36C32×#204C2212yescomplemented
37C32×ΓL(1,𝔽25)C2212yescomplemented
38C3×#3719C2212yescomplemented
39C3×#3716C2212yescomplemented
40C3×#3715C2212yescomplemented
41C3×#3711C2212yescomplemented
42C3×#3710C2211yescharacteristic
43C3×D3×#41—32no—
44C2×C3×D3×Q8—32no—
45#64319C2×C311yescharacteristic
46D32×Q8C2×C311yescharacteristic, complemented
47C32×#137—32no—
48Q16×C3⋊D3C2×C311yescharacteristic, complemented
49C3×#951—32no—
50C3×#942—32no—
51C3×#918—22no—
52C3×#918—32no—
53C3×#918D312yescomplemented
54C3×#918C2×C312yescomplemented
55C3×D3×Q16—32no—
56C3×D3×Q16—32no—
57C3×D3×Q16—61no—
58C3×#915—32no—
59C3×#915—32no—
60C3×D3×SD16—32no—
61C3×D3×SD16—32no—
62C3×#909—32no—
63C3×D3×M16—32no—
64#63946C2×C312yescomplemented
65#63944C2×C311yescharacteristic, complemented
66#63943C2×C312yescomplemented
67#63940C2×C311yescharacteristic, complemented
68#63800C2×C312yescomplemented
69#63796C2×C311yescharacteristic, complemented
70#63791C2×C311yescharacteristic, complemented
71C2×C3×D32—21no—
72C2×C3×D32D411yescharacteristic
73C33×Q8C2311yescharacteristic
74C33×Q8C2311yescharacteristic
75C3×C4×C3⋊D3—21no—
76C3×C4×C3⋊D3—21no—
77C3×C4×C3⋊D3C2311yescharacteristic
78C3×#634—21no—
79C3×#634—21no—
80C3×#634C2311yescharacteristic
81C3×#634C2311yescharacteristic
82C32×D12—22no—
83C32×D12C2312yes—
84C32×C4×D3—22no—
85C32×C4×D3—22no—
86C32×C4×D3C2312yes—
87C32×Dic6—22no—
88C32×Dic6C2312yes—
89C3×#627—21no—
90C3×#627—22no—
91C3×#625—22no—
92C3×#625—21no—
93C3×#624—21no—
94C3×#624D411yescharacteristic
95C3×D3×Dic3—22no—
96C3×D3×Dic3—22no—
97C3×D3×Dic3D412yes—
98C33×C8C2311yescharacteristic
99C3×C3⋊(C3⋊C8)C2311yescharacteristic
100C32×C3⋊C8C2312yes—
101C2×C3×#137—91no—
102D3×#137—32no—
103C32×#41—32no—
104C2×C32×Q8—32no—
105Q8×C3⋊D3C22×C311yescharacteristic
106Q8×C3⋊D3C22×C311yescharacteristic
107C3×#239—22no—
108C3×#239C2×D312yes—
109C3×#239C22×C312yes—
110C3×D3×Q8—22no—
111C3×D3×Q8—32no—
112C3×D3×Q8—32no—
113C3×D3×Q8—32no—
114C3×D3×Q8—32no—
115C3×D3×Q8—62no—
116C3×D3×Q8—62no—
117C3×D3×Q8—61no—
118C3×D3×Q8—61no—
119C3×D3×Q8C2×D312yescomplemented
120C3×D3×Q8C22×C312yescomplemented
121C3×#237—32no—
122C3×#237—62no—
123C3×D3×D4—32no—
124C3×D3×D4—62no—
125C3×#235—32no—
126C3×#235—62no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—62no—
129C2×C3×C4×D3—62no—
130C2×C3×Dic6—32no—
131C2×C3×Dic6—62no—
132#3802—21no—
133#3802C22×C311yescharacteristic
134C4×D32—21no—
135C4×D32—21no—
136C4×D32C22×C311yescharacteristic
137#3797—21no—
138#3797C22×C311yescharacteristic
139#3795—22no—
140#3795C22×C312yes—
141D3×Dic6—22no—
142D3×Dic6C22×C312yescomplemented
143C32×Q16—21no—
144C32×Q16—22no—
145C32×Q16—32no—
146C32×Q16—41no—
147C32×Q16C2×D312yescomplemented
148C32×Q16C22×C311yescharacteristic, complemented
149C32×SD16—32no—
150C32×SD16—32no—
151C32×M16—32no—
152#3756C22×C311yescharacteristic, complemented
153#3756C22×C311yescharacteristic, complemented
154#3746C22×C311yescharacteristic, complemented
155C8×C3⋊D3C22×C311yescharacteristic
156C3×#216—22no—
157C3×#216—32no—
158C3×#216—32no—
159C3×#216—32no—
160C3×#216—61no—
161C3×#216—61no—
162C3×#216C2×D312yescomplemented
163C3×#216C22×C312yescomplemented
164C3×#215—22no—
165C3×#215—32no—
166C3×#215C2×D312yescomplemented
167C3×#215C22×C312yescomplemented
168C3×#214—32no—
169C3×#214—32no—
170C3×#208—32no—
171C3×Dic12—32no—
172C3×Dic12—32no—
173C3×Dic12—61no—
174C3×#204—22no—
175C3×#204—32no—
176C3×#204C2×D312yescomplemented
177C3×#204C22×C312yescomplemented
178C3×ΓL(1,𝔽25)—22no—
179C3×ΓL(1,𝔽25)—32no—
180C3×ΓL(1,𝔽25)C2×D312yescomplemented
181C3×ΓL(1,𝔽25)C22×C312yescomplemented
182C3×D3×C8—32no—
183C3×D3×C8—32no—
184C3×D3×C8—61no—
185#3719C22×C312yescomplemented
186#3716C22×C312yescomplemented
187#3715C22×C312yescomplemented
188#3711C22×C312yescomplemented
189#3710C22×C311yescharacteristic
190C2×C3×C3⋊D3C2×D411yescharacteristic
191C2×C32×D3—22no—
192C2×C32×D3C2×D412yes—
193C3×D32—22no—
194C3×D32—42no—
195C33×C4—21no—
196C33×C4—21no—
197C33×C4C2411yescharacteristic
198C3×C3⋊Dic3—21no—
199C3×C3⋊Dic3—21no—
200C3×C3⋊Dic3C2×D411yescharacteristic
201C32×Dic3—22no—
202C32×Dic3C2×D412yes—
203C2×C3×#41—91no—
204C22×C3×Q8—91no—
205D3×#41—32no—
206C2×D3×Q8—32no—
207C3×#137—32no—
208C3×#137—32no—
209C3×#137—62no—
210C3×#137—92no—
211C3×#137—92no—
212C3×#137—92no—
213C2×C3×Q16—91no—
214C2×C3×Q16—91no—
215C2×C3×SD16—91no—
216C2×C3×SD16—91no—
217C2×C3×M16—91no—
218#951—32no—
219#942—32no—
220#918—32no—
221#918C3×D312yescomplemented
222D3×Q16—32no—
223D3×Q16—32no—
224D3×Q16—61no—
225#915—32no—
226#915—32no—
227D3×SD16—32no—
228D3×SD16—32no—
229#909—32no—
230D3×M16—32no—
231C22×C3×D3—32no—
232C22×C3×D3—62no—
233C2×D32—21no—
234C2×D32C3×D411yescharacteristic
235C32×Q8—21no—
236C32×Q8—21no—
237C32×Q8—22no—
238C32×Q8—22no—
239C32×Q8—32no—
240C32×Q8—41no—
241C32×Q8—41no—
242C32×Q8—62no—
243C32×Q8C22×D312yes—
244C32×Q8C22×D312yes—
245C32×Q8C23×C311yescharacteristic
246C32×Q8C23×C311yescharacteristic
247C32×D4—32no—
248C32×D4—62no—
249C2×C32×C4—32no—
250C2×C32×C4—62no—
251C2×C32×C4—62no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3C23×C311yescharacteristic
255#634—21no—
256#634—21no—
257#634C23×C311yescharacteristic
258#634C23×C311yescharacteristic
259C3×#67—62no—
260C3×#67—62no—
261C3×#67—62no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—62no—
264C2×C3×Dic3—62no—
265C3×D12—22no—
266C3×D12—22no—
267C3×D12—22no—
268C3×D12—42no—
269C3×D12C22×D312yes—
270C3×D12C23×C312yes—
271C3×C4×D3—22no—
272C3×C4×D3—22no—
273C3×C4×D3—22no—
274C3×C4×D3—22no—
275C3×C4×D3—22no—
276C3×C4×D3—32no—
277C3×C4×D3—32no—
278C3×C4×D3—32no—
279C3×C4×D3—42no—
280C3×C4×D3—42no—
281C3×C4×D3—61no—
282C3×C4×D3—62no—
283C3×C4×D3—62no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—121no—
288C3×C4×D3—121no—
289C3×C4×D3C22×D312yes—
290C3×C4×D3C23×C312yes—
291C3×Dic6—22no—
292C3×Dic6—22no—
293C3×Dic6—22no—
294C3×Dic6—32no—
295C3×Dic6—32no—
296C3×Dic6—42no—
297C3×Dic6—61no—
298C3×Dic6—61no—
299C3×Dic6—62no—
300C3×Dic6—62no—
301C3×Dic6—62no—
302C3×Dic6—62no—
303C3×Dic6—62no—
304C3×Dic6—121no—
305C3×Dic6—121no—
306C3×Dic6C22×D312yes—
307C3×Dic6C23×C312yes—
308#627—21no—
309#627—22no—
310#625—22no—
311#625—21no—
312#624—21no—
313#624C3×D411yescharacteristic
314D3×Dic3—22no—
315D3×Dic3—22no—
316D3×Dic3C3×D412yes—
317C32×C8—21no—
318C32×C8—22no—
319C32×C8—32no—
320C32×C8—41no—
321C32×C8C22×D312yes—
322C32×C8C23×C311yescharacteristic
323C3⋊(C3⋊C8)C23×C311yescharacteristic
324C3×C3⋊C8—22no—
325C3×C3⋊C8—32no—
326C3×C3⋊C8—61no—
327C3×C3⋊C8C22×D312yes—
328C3×C3⋊C8C23×C312yes—
329C2×#137—91noSylow
330C2×C33C22×D411yescharacteristic
331C3×C3⋊D3#13712yescomplemented
332C32×D3—22no—
333C32×D3—42no—
334C3×#41—32no—
335C3×#41—32no—
336C3×#41—62no—
337C3×#41—92no—
338C3×#41—182no—
339C2×C3×Q8—32no—
340C2×C3×Q8—32no—
341C2×C3×Q8—62no—
342C2×C3×Q8—92no—
343C2×C3×Q8—91no—
344C2×C3×Q8—91no—
345C2×C3×Q8—91no—
346C2×C3×Q8—182no—
347C2×C3×Q8—181no—
348C2×C3×D4—91no—
349C2×C3×D4—181no—
350C22×C3×C4—91no—
351C22×C3×C4—181no—
352C22×C3×C4—181no—
353#239C2×C3×D312yes—
354D3×Q8—32no—
355D3×Q8—32no—
356D3×Q8—32no—
357D3×Q8—32no—
358D3×Q8—61no—
359D3×Q8—61no—
360D3×Q8—62no—
361D3×Q8—62no—
362D3×Q8C2×C3×D312yescomplemented
363#237—32no—
364#237—62no—
365D3×D4—32no—
366D3×D4—62no—
367#235—32no—
368#235—62no—
369C2×C4×D3—32no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×Dic6—32no—
373C2×Dic6—62no—
374C3×Q16—21no—
375C3×Q16—22no—
376C3×Q16—32no—
377C3×Q16—32no—
378C3×Q16—41no—
379C3×Q16—62no—
380C3×Q16—92no—
381C3×Q16—91no—
382C3×Q16—91no—
383C3×Q16—91no—
384C3×Q16D3211yescharacteristic, complemented
385C3×Q16C2×C3×D312yescomplemented
386C3×SD16—32no—
387C3×SD16—32no—
388C3×SD16—32no—
389C3×SD16—32no—
390C3×SD16—62no—
391C3×SD16—62no—
392C3×SD16—92no—
393C3×SD16—92no—
394C3×M16—32no—
395C3×M16—32no—
396C3×M16—62no—
397C3×M16—92no—
398C2×C3×C8—91no—
399C2×C3×C8—91no—
400#216—32no—
401#216—32no—
402#216—32no—
403#216—61no—
404#216—61no—
405#216C2×C3×D312yescomplemented
406#215—32no—
407#215C2×C3×D312yescomplemented
408#214—32no—
409#214—32no—
410#208—32no—
411Dic12—32no—
412Dic12—32no—
413Dic12—61no—
414#204—32no—
415#204C2×C3×D312yescomplemented
416ΓL(1,𝔽25)—32no—
417ΓL(1,𝔽25)C2×C3×D312yescomplemented
418D3×C8—32no—
419D3×C8—32no—
420D3×C8—61no—
421C22×C32—32no—
422C22×C32—62no—
423C2×C3⋊D3C2×C3×D411yescharacteristic
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—32no—
428C2×C3×D3—42no—
429C2×C3×D3—61no—
430C2×C3×D3—64no—
431C2×C3×D3—124no—
432C2×C3×D3D3×D412yes—
433C2×C3×D3C2×C3×D412yes—
434D32—22no—
435D32—42no—
436C32×C4—22no—
437C32×C4—22no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—22no—
442C32×C4—32no—
443C32×C4—41no—
444C32×C4—42no—
445C32×C4—41no—
446C32×C4—41no—
447C32×C4—42no—
448C32×C4—62no—
449C32×C4—81no—
450C32×C4—81no—
451C32×C4C23×D312yes—
452C32×C4C24×C311yescharacteristic
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3C2×C3×D411yescharacteristic
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—32no—
460C3×Dic3—42no—
461C3×Dic3—61no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—121no—
465C3×Dic3—121no—
466C3×Dic3D3×D412yes—
467C3×Dic3C2×C3×D412yes—
468C2×#41—91no—
469C22×Q8—91no—
470#137—32no—
471#137—92no—
472#137—92no—
473#137—92no—
474C2×Q16—91no—
475C2×Q16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×M16—91no—
479C33C2×#13711yescharacteristic, complemented, Sylow
480C23×C3—91no—
481C23×C3—181no—
482C22×D3—32no—
483C22×D3—62no—
484C3×Q8—22no—
485C3×Q8—22no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—32no—
489C3×Q8—32no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—62no—
493C3×Q8—62no—
494C3×Q8—62no—
495C3×Q8—91no—
496C3×Q8—91no—
497C3×Q8—122no—
498C3×Q8—181no—
499C3×Q8—181no—
500C3×Q8—182no—
501C3×Q8—181no—
502C3×Q8C2×D3211yescharacteristic
503C3×Q8C2×D3211yescharacteristic
504C3×Q8C22×C3×D312yes—
505C3×Q8C22×C3×D312yes—
506C3×D4—32no—
507C3×D4—32no—
508C3×D4—62no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—122no—
512C3×D4—181no—
513C3×D4—182no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—91no—
522C2×C3×C4—92no—
523C2×C3×C4—91no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—181no—
527C2×C3×C4—181no—
528C2×C3×C4—182no—
529C2×C3×C4—181no—
530C2×C3×C4—182no—
531#67—62no—
532#67—62no—
533#67—62no—
534C2×Dic3—32no—
535C2×Dic3—62no—
536C2×Dic3—62no—
537D12—22no—
538D12C22×C3×D312yes—
539C4×D3—22no—
540C4×D3—22no—
541C4×D3—32no—
542C4×D3—32no—
543C4×D3—32no—
544C4×D3—61no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3C22×C3×D312yes—
553Dic6—22no—
554Dic6—32no—
555Dic6—32no—
556Dic6—61no—
557Dic6—61no—
558Dic6—62no—
559Dic6—62no—
560Dic6—62no—
561Dic6—62no—
562Dic6—62no—
563Dic6—121no—
564Dic6—121no—
565Dic6C22×C3×D312yes—
566C3×C8—22no—
567C3×C8—21no—
568C3×C8—32no—
569C3×C8—32no—
570C3×C8—41no—
571C3×C8—62no—
572C3×C8—91no—
573C3×C8C2×D3211yescharacteristic
574C3×C8C22×C3×D312yes—
575C3⋊C8—32no—
576C3⋊C8—61no—
577C3⋊C8C22×C3×D312yes—
578C2×C32—21no—
579C2×C32—22no—
580C2×C32—41no—
581C2×C32—62no—
582C2×C32—122no—
583C2×C32C2×D3×D412yes—
584C2×C32C22×C3×D411yescharacteristic
585C3⋊D3C3×#13712yescomplemented
586C3×D3—22no—
587C3×D3—22no—
588C3×D3—34no—
589C3×D3—42no—
590C3×D3—42no—
591C3×D3—42no—
592C3×D3—62no—
593C3×D3—82no—
594#41—32no—
595#41—92no—
596#41—182no—
597C2×Q8—32no—
598C2×Q8—92no—
599C2×Q8—91no—
600C2×Q8—91no—
601C2×Q8—91no—
602C2×Q8—182no—
603C2×Q8—181no—
604C2×D4—91no—
605C2×D4—181no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609Q16—32no—
610Q16—92no—
611Q16—91no—
612Q16—91no—
613Q16—91no—
614Q16C3×D3211yescharacteristic, complemented
615SD16—32no—
616SD16—32no—
617SD16—92no—
618SD16—92no—
619M16—32no—
620M16—92no—
621C2×C8—91no—
622C2×C8—91no—
623C22×C3—32no—
624C22×C3—32no—
625C22×C3—62no—
626C22×C3—62no—
627C22×C3—62no—
628C22×C3—91no—
629C22×C3—122no—
630C22×C3—182no—
631C22×C3—362no—
632C2×D3—22no—
633C2×D3—32no—
634C2×D3—61no—
635C2×D3—64no—
636C2×D3—124no—
637C2×D3C3×D3×D412yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—32no—
645C3×C4—32no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—91no—
657C3×C4—122no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4C22×D3211yescharacteristic
661C3×C4C23×C3×D312yes—
662Dic3—22no—
663Dic3—32no—
664Dic3—61no—
665Dic3—62no—
666Dic3—62no—
667Dic3—121no—
668Dic3—121no—
669Dic3C3×D3×D412yes—
670C32—22no—
671C32—21no—
672C32—41no—
673C32D3×#13712yescomplemented
674C32C2×C3×#13711yescharacteristic, complemented
675C23—91no—
676C23—181no—
677Q8—32no—
678Q8—62no—
679Q8—91no—
680Q8—91no—
681Q8—181no—
682Q8—181no—
683Q8—182no—
684Q8—181no—
685Q8C2×C3×D3211yescharacteristic
686Q8C2×C3×D3211yescharacteristic
687D4—32no—
688D4—62no—
689D4—181no—
690D4—182no—
691C2×C4—32no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—91no—
695C2×C4—92no—
696C2×C4—91no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—182no—
700C2×C4—181no—
701C2×C4—182no—
702C8—32no—
703C8—91no—
704C8C2×C3×D3211yescharacteristic
705C2×C3—21no—
706C2×C3—22no—
707C2×C3—41no—
708C2×C3—62no—
709C2×C3—62no—
710C2×C3—92no—
711C2×C3—122no—
712C2×C3—122no—
713C2×C3—122no—
714C2×C3—242no—
715C2×C3D32×D411yescharacteristic
716C2×C3C2×C3×D3×D412yes—
717D3—22no—
718D3—34no—
719D3—42no—
720D3—62no—
721C22—32no—
722C22—62no—
723C22—91no—
724C22—182no—
725C22—362no—
726C4—21no—
727C4—21no—
728C4—32no—
729C4—62no—
730C4—91no—
731C4—181no—
732C4—181no—
733C4C22×C3×D3211yescharacteristic
734C3—21no—
735C3—22no—
736C3—41no—
737C3#1059476011yescharacteristic, direct product factor
738C3C3×D3×#13712yescomplemented
739C2—62no—
740C2—92no—
741C2—122no—
742C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×Q16C22
socleC2×C33C22×D4
prime radicalC3×#64319C2
hypercenterC3×Q16D32
hypocenterC32C2×C3×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×D32×Q8C2semidirect
3. C3×Q16×C3⋊D3C2semidirect
4. C32×#918C2semidirect
5. C3×#63946C2semidirect
6. C3×#63944C2semidirect
7. C3×#63943C2semidirect
8. C3×#63940C2semidirect
9. C3×#63800C2semidirect
10. C3×#63796C2semidirect
11. C3×#63791C2semidirect
13. #10594760C3direct (N × H)
17. C32×D3×Q8C22semidirect
28. C3×D3×Dic6C22semidirect
29. C33×Q16C22semidirect
30. C3×#3756C22semidirect
31. C3×#3756C22semidirect
32. C3×#3746C22semidirect
34. C32×#216C22semidirect
35. C32×#215C22semidirect
36. C32×#204C22semidirect
37. C32×ΓL(1,𝔽25)C22semidirect
38. C3×#3719C22semidirect
39. C3×#3716C22semidirect
40. C3×#3715C22semidirect
41. C3×#3711C22semidirect
46. D32×Q8C2×C3semidirect
48. Q16×C3⋊D3C2×C3semidirect
53. C3×#918D3semidirect
54. C3×#918C2×C3semidirect
64. #63946C2×C3semidirect
65. #63944C2×C3semidirect
66. #63943C2×C3semidirect
67. #63940C2×C3semidirect
68. #63800C2×C3semidirect
69. #63796C2×C3semidirect
70. #63791C2×C3semidirect
119. C3×D3×Q8C2×D3semidirect
120. C3×D3×Q8C22×C3semidirect
142. D3×Dic6C22×C3semidirect
147. C32×Q16C2×D3semidirect
148. C32×Q16C22×C3semidirect
152. #3756C22×C3semidirect
153. #3756C22×C3semidirect
154. #3746C22×C3semidirect
162. C3×#216C2×D3semidirect
163. C3×#216C22×C3semidirect
166. C3×#215C2×D3semidirect
167. C3×#215C22×C3semidirect
176. C3×#204C2×D3semidirect
177. C3×#204C22×C3semidirect
180. C3×ΓL(1,𝔽25)C2×D3semidirect
181. C3×ΓL(1,𝔽25)C22×C3semidirect
185. #3719C22×C3semidirect
186. #3716C22×C3semidirect
187. #3715C22×C3semidirect
188. #3711C22×C3semidirect
221. #918C3×D3semidirect
331. C3×C3⋊D3#137semidirect
362. D3×Q8C2×C3×D3semidirect
384. C3×Q16D32semidirect
385. C3×Q16C2×C3×D3semidirect
405. #216C2×C3×D3semidirect
407. #215C2×C3×D3semidirect
415. #204C2×C3×D3semidirect
417. ΓL(1,𝔽25)C2×C3×D3semidirect
479. C33C2×#137semidirect
585. C3⋊D3C3×#137semidirect
614. Q16C3×D32semidirect
673. C32D3×#137semidirect
674. C32C2×C3×#137semidirect
737. C3#10594760direct (N × H)
738. C3C3×D3×#137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#643192
C3×D32×Q82
C3×Q16×C3⋊D32
C32×#9182
C3×#639462
C3×#639442
C3×#639432
C3×#639402
C3×#638002
C3×#637962
C3×#637912
C3×D3×#1373
#105947603